磁场中轴向变速运动载流梁的参强联合共振

摘要/Abstract

摘要： 研究磁场环境中轴向变速运动载流梁在简谐激励作用下的参强联合共振问题，应用弹性力学理论、电磁场基本理论以及哈密顿变分原理，得到轴向变速运动载流梁的非线性磁弹性耦合振动方程。利用伽辽金积分法对其进行时间变量和空间变量的离散化，进而运用多尺度法以及坐标变换的方法求得系统主共振-主参数共振的幅频响应方程。通过算例，得到了系统随不同参数变化的幅频响应曲线图、时间历程图、相轨迹图、庞加莱映射图和共振系统的动相平面轨迹图，分析了轴向速度、轴向拉力、磁感应强度、电流密度及强迫激励对系统主共振-主参数共振特性的影响，结果表明系统呈现典型的非线性振动特征和复杂的动力学行为。

关键词: 载流梁, 主共振-主参数共振, 磁场, 轴向运动

Abstract: Combired parametric and forced resonance of an axially accelerating and current-carrying beam which was subjected to harmonic excitation under magnetic field was investigated. The elastic mechanics theory, electromagnetic field theory and Hamilton variational principle were applied to establish the nonlinear magnetoelastic coupling vibration equation of the axially accelerating and current-carrying beam. The time variables and the space variables were firstly discretized using Galerkin integral method, then multiscale method and coordinate transformation method were utilized and the amplitude-frequency response equation was obtained. Through calculation examples, the corresponding amplitude frequency response curves with different parameters, the time history response diagrams, phase plot, poincare map and dynamic phase trajectory graph of the resonance system were acquired and the effects of axial velocity, axial tension, magnetic induction intensity, electric current density and forced excitation on primary resonance-principal parametric resonance characteristics of the system were analyzed. The results show that the system presents typical nonlinear vibration characteristics and complex dynamics behavior.

Key words: current-carrying beam, primary resonance-principal parametric resonance, magnetic field, axial movement

中图分类号:

O322
O442

胡宇达, 戎艳天. 磁场中轴向变速运动载流梁的参强联合共振[J]. 中国机械工程.

Hu Yuda, Rong Yantian. Combined Parametric and Forced Resonance of an Axially Accelerating and Current-Carrying Beam under Magnetic Field[J]. China Mechanical Engineering.

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